Are there any formulae where an angle and e.g. the sin of an angle are added/subtracted together.
I know of infinite series such as,
$\sin\theta=\frac{\theta}{1}-\frac{\theta^3}{3!}+\frac{\theta^5}{5!}-...$
and approximations like,
$\cos\theta \approx 1-{\frac {\theta ^{2}}{2}}$
I am interested in exact finite formulae containing angles and trigonometric functions such as,
$\theta + a\sin k\theta $